CF1703F.Yet Another Problem About Pairs Satisfying an Inequality

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题目描述

You are given an array $a_1, a_2, \dots a_n$ . Count the number of pairs of indices $1 \leq i, j \leq n$ such that $a_i < i < a_j < j$ .

输入格式

The first line contains an integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases.

The first line of each test case contains an integer $n$ ( $2 \leq n \leq 2 \cdot 10^5$ ) — the length of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \leq a_i \leq 10^9$ ) — the elements of the array.

It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$ .

输出格式

For each test case, output a single integer — the number of pairs of indices satisfying the condition in the statement.

Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).

输入输出样例

输入#1

5
8
1 1 2 3 8 2 1 4
2
1 2
10
0 2 1 6 3 4 1 2 8 3
2
1 1000000000
3
0 1000000000 2

输出#1

说明/提示

For the first test cases the pairs are $(i, j)$ = $\{(2, 4), (2, 8), (3, 8)\}$ .

The pair $(2, 4)$ is true because $a_2 = 1$ , $a_4 = 3$ and $1 < 2 < 3 < 4$ .
The pair $(2, 8)$ is true because $a_2 = 1$ , $a_8 = 4$ and $1 < 2 < 4 < 8$ .
The pair $(3, 8)$ is true because $a_3 = 2$ , $a_8 = 4$ and $2 < 3 < 4 < 8$ .

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